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Calculus: Early Transcendentals

ISBN: 9780534362980 | 0534362982
Edition: 4th
Format: Paperback
Publisher: Brooks Cole
Pub. Date: 6/1/1999

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SummaryTable of Contents
These best-selling texts differ from CALCULUS, FOURTH EDITION in that the exponential and logarithmic functions are covered earlier. In the Fourth Edition CALCULUS, EARLY TRANSCENDENTALS these functions are introduced in the first chapter and their limits and derivatives are found in Chapters 2 and 3 at the same time as polynomials and other elementary functions. In this Fourth Edition, Stewart retains the focus on problem solving, the meticulous accuracy, the patient explanations, and the carefully graded problems that have made these texts word so well for a wide range of students. All new and unique features in CALCULUS, FOURTH EDITION have been incorporated into these revisions also.
A Preview of Calculus2(8)
Functions and Models
10(74)
Four Ways to Represent a Function
11(13)
... MORE
Mathematical Models
24(14)
New Functions from Old Functions
38(12)
Graphing Calculators and Computers
50(6)
Exponential Functions
56(8)
Inverse Functions and Logarithms
64(14)
Review
75(3)
Principles of Problem Solving
78(6)
Limits and Derivatives
84(96)
The Tangent and Velocity Problems
85(5)
The Limit of a Function
90(12)
Calculating Limits Using the Limit Laws
102(10)
The Precise Definition of a Limit
112(10)
Continuity
122(11)
Limits at Infinity; Horizontal Asymptotes
133(14)
Tangents, Velocities, and Other Rates of Change
147(9)
Derivatives
156(7)
Writing Project &box; Early Methods for Finding Tangents
162(1)
The Derivative as a Function
163(15)
Review
174(4)
Problems Plus
178(2)
Differentiation Rules
180(96)
Derivatives of Polynomials and Exponential Functions
181(9)
The Product and Quotient Rules
190(6)
Rates of Change in the Natural and Social Sciences
196(12)
Derivatives of Trigonometric Functions
208(7)
The Chain Rule
215(9)
Implicit Differentiation
224(9)
Higher Derivatives
233(7)
Applied Project &box; Where Should a Pilot Start Descent?
240(1)
Derivatives of Logarithmic Functions
240(6)
Hyperbolic Functions
246(7)
Related Rates
253(6)
Linear Approximations and Differentials
259(12)
Laboratory Project &box; Taylor Polynomials
266(1)
Review
267(4)
Problems Plus
271(5)
Applications of Differentiation
276(90)
Maximum and Minimum Values
277(11)
Applied Project &box; The Calculus of Rainbows
286(2)
The Mean Value Theorem
288(6)
How Derivatives Affect the Shape of a Graph
294(11)
Indeterminate Forms and L'Hospital's Rule
305(9)
Writing Project &box; The Origins of L'Hospital's Rule
313(1)
Summary of Curve Sketching
314(8)
Graphing with Calculus and Calculators
322(7)
Optimization Problems
329(11)
Applied Project &box; The Shape of a Can
339(1)
Applications to Economics
340(5)
Newton's Method
345(6)
Antiderivatives
351(12)
Review
359(4)
Problems Plus
363(3)
Integrals
366(66)
Areas and Distances
367(11)
The Definite Integral
378(13)
Discovery Project &box; Area Functions
390(1)
The Fundamental Theorem of Calculus
391(10)
Indefinite Integrals and the Total Change Theorem
401(9)
Writing Project &box; Newton, Leibniz, and the Invention of Calculus
409(1)
The Substitution Rule
410(8)
The Logarithm Defined as an Integral
418(11)
Review
425(4)
Problems Plus
429(3)
Applications of Integration
432(36)
Areas between Curves
433(7)
Volumes
440(11)
Volumes by Cylindrical Shells
451(5)
Work
456(4)
Average Value of a Function
460(5)
Applied Project &box; Where to Sit at the Movies
463(1)
Review
463(2)
Problems Plus
465(3)
Techniques of Integration
468(72)
Integration by Parts
469(7)
Trigonometric Integrals
476(7)
Trigonometric Substitution
483(7)
Integration of Rational Functions by Partial Fractions
490(9)
Strategy for Integration
499(6)
Integration Using Tables and Computer Algebra Systems
505(7)
Discovery Project &box; Patterns in Integrals
511(1)
Approximate Integration
512(11)
Improper Integrals
523(14)
Review
534(3)
Problems Plus
537(3)
Further Applications of Integration
540(40)
Arc Length
541(7)
Area of a Surface of Revolution
548(7)
Discovery Project &box; Rotating on a Slant
554(1)
Applications to Physics and Engineering
555(9)
Applications to Economics and Biology
564(5)
Probability
569(9)
Review
576(2)
Problems Plus
578(2)
Differential Equations
580(60)
Modeling with Differential Equations
581(5)
Direction Fields and Euler's Method
586(9)
Separable Equations
595(8)
Applied Project &box; Which Is Faster, Going Up or Coming Down?
602(1)
Exponential Growth and Decay
603(10)
Applied Project &box; Calculus and Baseball
612(1)
The Logistic Equation
613(9)
Linear Equations
622(6)
Predator-Prey Systems
628(10)
Review
634(4)
Problems Plus
638(2)
Parametric Equations and Polar Coordinates
640(52)
Curves Defined by Parametric Equations
641(7)
Laboratory Project &box; Families of Hypocycloids
648(1)
Tangents and Areas
648(7)
Laboratory Project &box; Bezier Curves
655(1)
Arc Length and Surface Area
655(13)
Polar Coordinates
668(102)
Areas and Lengths in Polar Coordinates
770(5)
Conic Sections
775(7)
Conic Sections in Polar Coordinates
782(8)
Review
788(2)
Problems Plus
790
Infinite Sequences and Series
692(90)
Sequences
693(11)
Laboratory Project &box; Logistic Sequences
704(1)
Series
704(10)
The Integral Test and Estimates of Sums
714(7)
The Comparison Tests
721(5)
Alternating Series
726(5)
Absolute Convergence and the Ratio and Root Tests
731(7)
Strategy for Testing Series
738(2)
Power Series
740(5)
Representations of Functions as Power Series
745(6)
Taylor and Maclaurin Series
751(11)
The Binomial Series
762(4)
Writing Project &box; How Newton Discovered the Binomial Series
765(1)
Applications of Taylor Polynomials
766(12)
Applied Project &box; Radiation from the Stars
774(1)
Review
775(3)
Problems Plus
778(4)
Vectors and the Geometry of Space
782(54)
Three-Dimensional Coordinate Systems
783(5)
Vectors
788(8)
The Dot Product
796(7)
The Cross Product
803(9)
Discovery Project &box; The Geometry of a Tetrahedron
811(1)
Equations of Lines and Planes
812(9)
Cylinders and Quadric Surfaces
821(6)
Cylindrical and Spherical Coordinates
827(8)
Laboratory Project &box; Families of Surfaces
832(1)
Review
832(3)
Problems Plus
835(1)
Vector Functions
836(36)
Vector Functions and Space Curves
837(6)
Derivatives and Integrals of Vector Functions
843(6)
Arc Length and Curvature
849(8)
Motion in Space: Velocity and Acceleration
857(13)
Applied Project &box; Kepler's Laws
866(1)
Review
867(3)
Problems Plus
870(2)
Partial Derivatives
872(94)
Functions of Several Variables
873(14)
Limits and Continuity
887(8)
Partial Derivatives
895(13)
Tangent Planes and Linear Approximations
908(9)
The Chain Rule
917(9)
Directional Derivatives and the Gradient Vector
926(13)
Maximum and Minimum Values
939(12)
Applied Project &box; Designing a Dumpster
949(1)
Discovery Project &box; Quadratic Approximations and Critical Points
950(1)
Lagrange Multipliers
951(13)
Applied Project &box; Rocket Science
958(1)
Applied Project &box; Hydro-Turbine Optimization
959(1)
Review
960(4)
Problems Plus
964(2)
Multiple Integrals
966(74)
Double Integrals over Rectangles
967(9)
Iterated Integrals
976(5)
Double Integrals over General Regions
981(8)
Double Integrals in Polar Coordinates
989(6)
Applications of Double Integrals
995(10)
Surface Area
1005(3)
Triple Integrals
1008(10)
Discovery Project &box; Volumes of Hyperspheres
1018(1)
Triple Integrals in Cylindrical and Spherical Coordinates
1018(8)
Applied Project &box; Roller Derby
1024(1)
Discovery Project &box; The Intersection of Three Cylinders
1025(1)
Change of Variables in Multiple Integrals
1026(12)
Review
1034(4)
Problems Plus
1038(2)
Vector Calculus
1040(84)
Vector Fields
1041(6)
Line Integrals
1047(12)
The Fundamental Theorem for Line Integrals
1059(9)
Green's Theorem
1068(7)
Curl and Divergence
1075(8)
Parametric Surfaces and Their Areas
1083(10)
Surface Integrals
1093(12)
Stokes' Theorem
1105(6)
Writing Project &box; Three Men and Two Theorems
1110(1)
The Divergence Theorem
1111(7)
Summary
1118(4)
Review
1119(3)
Problems Plus
1122(2)
Second-Order Differential Equations
1124(1)
Second-Order Linear Equations
1125(6)
Nonhomogeneous Linear Equations
1131(7)
Applications of Second-Order Differential Equations
1138(8)
Series Solutions
1146
Review
1150
AppendixesA1(1)
A Intervals, Inequalities, and Absolute Values
A2(1)
B Coordinate Geometry and Lines
A10(1)
C Graphs of Second-Degree Equations
A16(1)
D Trigonometry
A24(1)
E Sigma Notation
A37(1)
F Proofs of Theorems
A42(1)
G Complex Numbers
A52(1)
H Answers to Odd-Numbered Exercises
A60(1)
IndexA121

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